My brother recently got me interested in Minecraft, and I'm having a lot of fun playing it. The thing is, I've only ever played the Beta version. After I first played it, I found a whole bunch of pictures and videos online with stuff that wasn't in the version I was playing. So I was wondering: What are the main differences between all the different versions of the game?

What you might have seen is someone playing with mods - extra code not written by Mojang - that allow players to do things not in the base game.

As Minecraft auto updates (you get prompted until you accept the update) you will always be playing the latest released version (even though it's still in Beta). This means that you can be sure that when playing multiplayer everyone is on the same version.

There have been removals of "stuff" but mostly it's tweaks to existing game play plus additions of new game play.

Good answer. Very few blocks are missing from Beta (sponge, blue flowers, some colours of wool). Some blocks are in Beta but are just very rare (e.g. clay, diamond). Everything else is either added in by a game mod, or is actually an existing block with custom texture pack.
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Jonathan DrainSep 13 '11 at 18:44

Outside of various updates to the "Beta" version of Minecraft, there are two major versions of Minecraft at the moment.

Minecraft Beta, often called Alpha, or Survival in older videos, is the main game, where you enter an infinite world and explore, build, craft, and try to survive the night. It's the main focus of development by Mojang AB, and, for the most part, has the most features. The multiplayer version of this is often called SMP, for Survival MultiPlayer. This version has gone through many different iterations, and at the time of this post, will be entering version 1.8 very soon.

There is also Minecraft Classic, often called Creative, with a limited sized world, and access to a wide amount of blocks, with the ability to create and destroy blocks instantly. This version is free, and for a period of time, was the only version of the game out there. As of Minecraft Beta 1.8, it will be possible to create a world with the infinite block placement/destruction, while having access to the many other features added to the game since the original version.